Write the equation of a line parallel to the given line that passes through the point (- 5, 14) . y = 3/5 * x - 21.
1 answer:
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9514 1404 393
Answer:
(-5,1)
Step-by-step explanation:
To eliminate x, multiply the first equation by 3 and add 2 times the second equation.
3(-2x +7y) +2(3x -4y) = 3(17) +2(-19)
-6x +21y +6x -8y = 51 -38
13y = 13
y = 1 . . . . . matches the third answer choice
(x, y) = (-5, 1)
(1) See below for a diagram. Basically, the distance on the ground from the person to the building (34 ft) is adjacent to the angle of elevation (74 degrees) and the height of the building (labeled h in the diagram) is the side opposite the angle. Since we are dealing with opposite and adjacent we use the tangent of the angle and tan = opp/adj
Specifically,
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feet.
Please be sure your calculator is set to degrees (not radians) when you do this problem.
(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.
sin = opp/hyp. As the sin Q = 9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.
cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.
You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.
Specifically,
Please be sure your calculator is set to degrees (not radians) when you do this problem.
(2) Here since P & Q are complimentary it means that their sum is 90 degrees. Since this is a right triangle that means that the remaining angle (R) must be the right angle. See below for a diagram.
sin = opp/hyp. As the sin Q = 9/41 this means that 9 is the length of the side opposite Q (the side PR) and 41 is the length of the hypotenuse. This makes the remaining side (QR) 40 in length.
cos = adj/hyp. If we focus on angle P the side adjacent (next to) is 9 and the hypotenuse is 41. Thus the cos of P = 9/41.
You could have also realized that if P & Q are complimentary the sin P = cos Q and the cos P = sin Q. We were not asked about tangent but it is also the case that tan P = cot Q and cot P = tan Q.